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Math Help - Hypothesis Testing

  1. #1
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    Hypothesis Testing

    Hello,
    I am looking for any help in clarifying if I am on the right track, or help to put me on the right track. There is only 1 question with my answers for now, and I would really appreciate any input.
    Thank you in advance!

    Also for the question I have:
    -stated the null and alternative hypothesis
    -stated the critical region to reject or fail to reject the null
    -Identified the test stat
    -found the test stat
    -stated the conclusion.

    The question:

    A customer is in need of a large supply of copper tubing that is cut 1.25 meters long. A plumbing supply company guarantees that if you order a specified lenght, you will receive what you ordered within a standard deviation=0.0001. To test the companies guarantee, a sample of 10 pieces of the tubing was taken. The mean length of the tubing was 1.2502 meters. Assume the population is normally distributed.
    a)Is there a significant difference in the specified length of the tubing at the 0.01 significance level? Based on your answer, should the customer trust the guarantee?
    b)Calculate the p-value at the 0.01 significance level. Is it significant?

    My answers:

    Ho: u=1.25 H1: u=/=1.25
    Critical region: Fail to reject Ho if the test statistic falls between 2.33 and -2.33. Reject Ho if the test statistic does not fall between 2.33 and -2.33.
    z=6.3 with test stat=0.0001
    Conclusion: There is not sufficient sample evidence to warrant rejection of the claim that if you order a specified length of pipe, you will receive it within a standard deviation of 0.0001.
    a)No, there is not a significant difference in the length of tubing at the 0.01 significance level. The customer should trust the company's guarantee.
    b) P-value=0.0002 and it is not significant.
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  2. #2
    Super Member
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    London / Cambridge
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    So you have [LaTeX ERROR: Convert failed]

    Now I could be wrong here, but the manufactures claim is based on the accuracy of their cut. How I see if their cut is not so accurate you will get a variety of tubes shorter and longer than the required length so the average will always be pretty much the same. I reckon that you should have  H_0 : \sigma = 0.0001 \ \ \ \ H_1 : \sigma > 0.0001  .


    So want you want is to find c [LaTeX ERROR: Convert failed] note his is a two tailed test.

    use to symmetry of the distribution. to get.

    [LaTeX ERROR: Convert failed]



    then you transform to Z
    [LaTeX ERROR: Convert failed]

    [LaTeX ERROR: Convert failed]

    using tables I get

    [LaTeX ERROR: Convert failed]

    I'll put some values in now
    [LaTeX ERROR: Convert failed]

    giving [Math] c = 1.24974[/tex]
    and [Math] 2 \mu - c = 1.25026[/tex]

    so if the manufactures claim is true, 99% of the time we should get [LaTeX ERROR: Convert failed]

    1.2502 is within the range (only just) so we can trust their claim.
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  3. #3
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    Thank you for your reply.

    I thought however, that if > was used, its a right tailed test.

    Its all so confusing. And what is the c represent?
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  4. #4
    Super Member
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    London / Cambridge
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    Quote Originally Posted by Thatgirl View Post
    Thank you for your reply.

    I thought however, that if > was used, its a right tailed test.

    Its all so confusing. And what is the c represent?

    Does this very very badly drawn image make thing any more clear ?
    Attached Thumbnails Attached Thumbnails Hypothesis Testing-picture-1.png  
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  5. #5
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    Yes. I am still unsure as to why it is two-tailed and not one-tailed but after staring at this for awhile the rest of it makes sense.

    Thank you!!
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